Math 10/11 Honors Section 3.5 Cosecant Secant and Cotangent Functions
SECTION 3.5 COSECANT SECANT
AND COTANGENT FUNCTIONS
I)
REVIEW: RECIPROCAL FUNCTIONS y 
1
f  x

The reciprocal function takes the reciprocal of all the
y-coordinates of a function

When graphing a reciprocal function, there are a
three main steps:
PRACTICE: GIVEN THE
FOLLOWING
FUNCTION,
GRAPH THE RECIPROCAL
y
5
x
-5
0
5
-5
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Math 10/11 Honors Section 3.5 Cosecant Secant and Cotangent Functions
II) RECIPROCAL

OF
TRIGONOMETRIC FUNCTIONS
Cosecant is the reciprocal of the sine function
csc 
csc 

Secant is the reciprocal of the cosine function
sec 
sec 

Cotangent is the reciprocal of the tangent function
cot  
cot  
Ex: Determine the value of each expression to 3 decimal places
i) csc 225
ii) sec135
iv) csc  3.66 
iii) cot 2.27
 radian mode 
 radian mode 
III) GRAPHING COSECANT FUNCTION
y
2
x
0
p
2p
3p
4p
5p
-2



When sinθ=0 , you will get Vertical Asymptotes
When sinθ=1 or -1, you will get Common points
Take the reciprocal of each sub-domain


Y-coordinates are large  Reciprocal will be small
Y-coordinates are small  Reciprocal will be large
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2
Math 10/11 Honors Section 3.5 Cosecant Secant and Cotangent Functions
IV) GRAPHING SECANT FUNCTION
y
2
x
0
p
2p
3p
4p
5p
-2



When cosθ=0 , you will get Vertical Asymptotes
When cosθ=1 or -1, you will get Common points
Take the reciprocal of each sub-domain
Y-coordinates are large  Reciprocal will be small
Y-coordinates are small  Reciprocal will be large


V) GRAPHING COTANGENT FUNCTION
y
2
x
0
p
2p
3p
4p
5p
-2



V.A. from tanθ will become x-intercepts
When tanθ=0 , you will get Vertical Asymptotes
When tanθ=1 or -1, you will get Common points


Y-coordinates are large  Reciprocal will be small
Y-coordinates are small  Reciprocal will be large
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EX: INDICATE
THE
DOMAIN & RANGE
FOR EACH OF THE
FOLLOWING FUNCTIONS:
y
Domain :
2
i) y  csc
x
0
p
2p
3p
4p
Range :
-2
y
Domain :
2
ii) y  sec
x
0
p
2p
3p
4p
Range :
-2
y
Domain :
2
iii) y  cot 
x
0
p
2p
3p
4p
Range :
-2
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Math 10/11 Honors Section 3.5 Cosecant Secant and Cotangent Functions
EX: SOLVE
csc 
2
3
FOR Θ IN EACH OF THE FOLLOWING:
cot  
5
7
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